We study many-particle transport in randomly jammed packing of spheres at different particle Péclet numbers (𝑃𝑒∗). We demonstrate that a modified Nakagami-m function describes particle velocity probability distributions when particle deposition occurs. We assess the universality of said function through comparison against Lagrangian simulations of various particle types as well as experimental data from the literature. We construe the function's physical meaning as its ability to explain particle deposition in terms of 𝑃𝑒∗ and the competition between distributions of energy barriers for particle release and particles' diffusive energy.